Decomposability conditions for compatible relations

Languages and compatible relations on monoids ∗

With every monoid, one can associate various binary relations, in particular the so-called principal quasi-order, principal order and principal congruence. The aim of this paper is to show that any compatible quasiorder, order and congruence can be obtained as an intersection of the corresponding principal relations. The particular case of languages -subsets of free monoids generated by an alph...

Counting the Relations Compatible with an Algebra

We investigate when a finite algebra admits only a finite number of compatible relations (modulo a natural equivalence). This finiteness condition is closely related to others in the literature, and arises naturally in duality theory. We find necessary conditions for a finite algebra to admit only finitely many compatible relations, as well as a family of examples of such algebras. The classic ...

Some Fixed Point Theorems for Weakly Compatible Multivalued Mappings Satisfying Some General Contractive Conditions of Integral Type

Some Relations among Values, Interactions, and Decomposability of Non-Additive Measures

We will discuss some relations among values, i.e., global/overall importance of each single element of the object to be considered, interaction indices, i.e., simultaneous interaction among the elements in a coalition, and inclusion-exclusion coverings, i.e., decomposability of non-additive measures and/or of the Choquet integral. So, we show that inclusion-exclusion coverings are characterized...

Generalized decomposability notions for first-order theories

This paper introduces the notion of decomposability in an extension and relative decomposability for first-order theories. We describe several basic facts connected with these notions and formulate a criterion of relative decomposability.